Global Prescribed Performance Control of Unknown Strict-Feedback Systems With Quantized References

This article is concerned with the global prescribed performance tracking control problem for strict-feedback systems with quantized references, unknown nonlinearities, and unmatched disturbances. Discontinuity appears frequently in such references, for which most nonlinear control or filtering methods are not applicable straightforward. Besides, the existing approaches of predefining tracking performance work under local initial conditions, available nonlinearity knowledge, disturbance-free cases, or have complexity issues. In this article, a novel smoothing function is first designed for the online automatic generation of smooth trajectories in place of the quantized reference. Then, the tangent barrier functions are combined with a new form of performance functions (inverse proportional functions) to form a control. The strong robustness of the resulting controller against model uncertainties and disturbances evades the need for approximation, observation, etc., yielding simplicity of the control. The new performance functions relax the specific initial condition. Their combination ensures for any initial condition, the tracking error converges to a given bound. Simulation results on vehicular platoons illustrate the theoretical findings.